Finite Group Databasebeta

← #49169037

Subgroups — #49169037

Order 37504.

394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036741C211yesmaximal, characteristic, complemented
2#34036470C212yesmaximal, complemented
3#34036429C212yesmaximal, complemented
4#34036334C212yesmaximal, complemented
5#34036280C212yesmaximal
6#34036229C212yesmaximal, complemented
7C4×#17989790C212yesmaximal, complemented
8#34036190C211yesmaximal, characteristic, complemented
9#518×C293C211yesmaximal, characteristic
10C2×#17989790C2212yes—
11C2×#17989790C2212yes—
12#22627624C2211yescharacteristic, complemented
13#22627617—22no—
14#22627616C2211yescharacteristic, complemented
15#22627614—22no—
16#22627603C2212yes—
17C4×Dic586C2212yescomplemented
18#22627557C2212yescomplemented
19#22627555C2212yescomplemented
20C4⋊#14556873C2212yescomplemented
21#22627547C2212yescomplemented
22#22627547C2212yescomplemented
23#22627545C2212yes—
24#22627545C2212yes—
25C22⋊#14556873C2212yes—
26#22627535C2211yescharacteristic, complemented
27C4×#14556873C2211yescharacteristic, complemented
28C22×D4×C293C2211yescharacteristic
29C4×D4×C293—22no—
30C4×D4×C293C2212yes—
31C4×D4×C293C2212yes—
32#117×C293C2211yescharacteristic
33#117×C293C2211yescharacteristic
34C2×C22⋊C4×C293—22no—
35C2×Dic586C2312yes—
36#17989790—24no—
37#17989790—24no—
38C2×#14556873C2312yes—
39C2×#14556873C2312yes—
40C4⋊Dic293—22no—
41C4⋊Dic293C2312yes—
42#17989781—22no—
43#17989781—22no—
44#17989781—22no—
45C22⋊Dic293—22no—
46C4×Dic293—22no—
47C24×C293—21no—
48C2×D4×C293—24no—
49C2×D4×C293—21no—
50C2×D4×C293C2312yes—
51C22×C4×C293—22no—
52C22×C4×C293—22no—
53C22×C4×C293C2311yescharacteristic
54C4⋊C4×C293D412yes—
55C4⋊C4×C293C2312yes—
56C22⋊C4×C293—21no—
57C22⋊C4×C293—22no—
58C22⋊C4×C293—22no—
59C22⋊C4×C293D412yes—
60C42×C293—21no—
61C42×C293C2311yescharacteristic
62C42×C293C2311yescharacteristic
63Dic586—22no—
64Dic586—22no—
65C2×Dic293—22no—
66C2×Dic293—22no—
67#14556873—22no—
68#14556873—22no—
69C23×C293—24no—
70C23×C293—22no—
71C23×C293—82no—
72C23×C293C2×D411yescharacteristic
73D4×C293—24no—
74D4×C293—22no—
75D4×C293#4114yes—
76C2×C4×C293—22no—
77C2×C4×C293—22no—
78C2×C4×C293—82no—
79C2×C4×C293—82no—
80C2×C4×C293C2×D411yescharacteristic
81C2×C4×C293C2×D412yes—
82C2×C4×C293C2×D412yes—
83C2×C4×C293C2411yescharacteristic
84C22×C293—21no—
85C22×C293—24no—
86C22×C293—22no—
87C22×C293—42no—
88C22×C293—42no—
89C22×C293—84no—
90C22×C293C22×D411yescharacteristic
91C4×C293—21no—
92C4×C293—22no—
93C4×C293—22no—
94C4×C293—42no—
95C4×C293C2×#4112yes—
96Dic293—42no—
97Dic293—42no—
98C2×C293—41no—
99C2×C293—44no—
100C2×C293#52511yescharacteristic
101C2×C293#57712yes—
102C293#312311yescharacteristic, complemented, Sylow
103#3123—2931nomaximal, Sylow
104#541—2931no—
105#518D29311yescharacteristic
106#485—2932no—
107#478—2932no—
108#461—2932no—
109#450—2932no—
110#440—2932no—
111C4×SD16—2932no—
112#433—2931no—
113C22×D4C2×D29311yescharacteristic
114C2×SD16—2932no—
115C2×SD16—2932no—
116C4⋊Q8—2931no—
117#126—5862no—
118#125—2931no—
119#125—5862no—
120C22⋊Q8—2932no—
121C4×Q8—2932no—
122C4×D4—22no—
123C4×D4C2×D29312yes—
124C4×D4C2×D29312yes—
125#117C2×D29311yescharacteristic
126#117C2×D29311yescharacteristic
127C2×C22⋊C4—22no—
128#107—2932no—
129#106—2932no—
130C4⋊C8—2932no—
131#103—2932no—
132#103—2932no—
133#102—2932no—
134#102—2932no—
135C22⋊C8—2932no—
136#97—2931no—
137C4×C8—2931no—
138C24—21no—
139C2×Q8—2932no—
140C2×D4—24no—
141C2×D4—21no—
142C2×D4C22×D29312yes—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4C22×D29311yescharacteristic
146SD16—5864no—
147SD16—5864no—
148C2×C8—2932no—
149C2×C8—2932no—
150C4⋊C4—2932no—
151C4⋊C4—5862no—
152C4⋊C4—5862no—
153C4⋊C4—5862no—
154C4⋊C4—5862no—
155C4⋊C4C22⋊D29312yes—
156C4⋊C4C22×D29312yes—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—5862no—
161C22⋊C4C22⋊D29312yes—
162C42—21no—
163C42—5862no—
164C42C22×D29311yescharacteristic
165C42C22×D29311yescharacteristic
166C23—24no—
167C23—22no—
168C23—82no—
169C23C2×C22⋊D29311yescharacteristic
170Q8—5862no—
171Q8—5862no—
172D4—24no—
173D4—22no—
174D4#1798980214yes—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—5862no—
180C2×C4—5862no—
181C2×C4C2×C22⋊D29311yescharacteristic
182C2×C4C2×C22⋊D29312yes—
183C2×C4C2×C22⋊D29312yes—
184C2×C4C23×D29311yescharacteristic
185C8—5862no—
186C8—5862no—
187C22—21no—
188C22—24no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—84no—
193C22C22×C22⋊D29311yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—11722no—
199C4—11722no—
200C4C2×#1798980212yes—
201C2—41no—
202C2—44no—
203C2#3403664011yescharacteristic
204C2#3403694012yes—
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#518×C293C2
socleC22×C293C22×D4
prime radicalC22×D4×C293C22
hypercenter#518D293
hypocenterC293#3123
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #34036741C2semidirect
2. #34036470C2semidirect
3. #34036429C2semidirect
4. #34036334C2semidirect
6. #34036229C2semidirect
7. C4×#17989790C2semidirect
8. #34036190C2semidirect
12. #22627624C22semidirect
14. #22627616C22semidirect
17. C4×Dic586C22semidirect
18. #22627557C22semidirect
19. #22627555C22semidirect
20. C4⋊#14556873C22semidirect
21. #22627547C22semidirect
22. #22627547C22semidirect
26. #22627535C22semidirect
27. C4×#14556873C22semidirect
102. C293#3123semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#340367412
#340364702
#340364292
#340363342
#340362802
#340362292
C4×#179897902
#340361902
#518×C2932
#3123293